[lkcl]

Zitat von Hawkwind

I think that you have got this wrong: (1.7) in the paper describes a so-called gauge transformation which acts on the gauge fields of QCD ("gluons"). There are no quark fields in this equation. Quarks are represented by spinors, see eq. (1.6); the psi there is a quark field.

spinor is a vector. okaaay. so what (in actual vectors) would the various quarks be?

btw i realised my mistake soon after posting, that gluons are the phase-changes *between* quarks. they are the means by which one quark may *transform* to another quark, representing the simultaneous phase-coherent energy required to *cancel* one and *replace* it with the other.

which is where the perspective of the rishon model comes into play.

QCD is a theory of gluons and quarks, it doesn't know about pions.
It's true that pions and gluons arrange in octets. However, the background is completely different: while gluons are octets in the space of the color quantum number ("red", "green", "blue"), pions on the other hand are octets in flavor space (flavors are "up", "down", "strange"). There is no relation between these representations.

Representations of baryons in flavor space are for instance described here:
http://www.ks.uiuc.edu/Services/Clas..._PDF/chp12.pdf

very much appreciated that link, it is clear and consice.

i'd like to tell you a story if i may, it will help somewhat to give some context. imagine that i am from a different world, with different language and expertise. i decide to go travelling the universe and i come across a world which, from the outside, looks like a buckminster fullerene. i can see that from the distance because it kept changing, the overlapping triangles and squares alternating as it rotated. my world is quite advanced in its engineering but is lacking in important scientific areas, hence my expedition.

as i approach i realise that there are people living *inside* the buckminster fullerene. i do some searches on radio frequencies and find something, then spend some time deciphering their language as best i can. mostly it is questions, "how do we work out the {squiggle,squiggle}" untranslateable and from what i can gather it is hugely technical discussions, very very advanced.

excitedly i learn more and am ready to approach and make "first contact". after landing my ship inside on one of the vertices of the buckyball. i approach people tentatively, and, haltingly in their language i wish to say "hello, i come from outer space".

at that point i realise that there *is* no word in their language for "outer space". i see no evidence of space travel. so i use the word "out there" and i get... blank stares. i realise that they *have* no concept even of "outside or living away from the surface of the buckyball".

now, i would *really like* to explain to them that they're living on a buckyball (which i cannot do without first explaining the concept of outer space). i cannot yet talk to them about geometry or geometric perspective because their maths is fantastically complex, in a totally alien language and *at the same time* is from the *subjective* viewpoint *solely and exclusively from the inside of a buckyball*.

so with that story in mind, as a very accurate analogy for our respective levels of expertise and ways of modelling our understanding of the world around us, please excuse me for asking questions in your world where the answers may take me some time to comprehend, and thank you so much for your patience.

now, from that "outside perspective" (encapsulated in the extended rishon model) i believe the difference between a pion and a gluon to simply be that the pion-superimposed-phase-coherent-photon(s)-wave-construct has "escaped" to become a stable particle, and that a gluon-superimposed-phase-coherent-photon(s)-wave-construct gets absolutely NO chance to do that. it's created and destroyed LITERALLY in less time than a single wavelength. actually probably under half the wavelength.

so from the perspective of all particles simply being mobius elliptically-polarised light, there *is* no difference between the cosine wave that superimposes on sin(theta - 90). to take an analogy: you can call sin(theta - 90) the "gluon" and cos (theta) the "pion" if you like but from a *photon-wave-form* perspective they are the same thing.

so perhaps a better way to put the question would be this: from joy walker's paper in which he makes good use of Friedmann-Robertson-Walker spacetime, i am aware that SU(2)xU(1) may be expressed as the multiplication of two exponentials. if the formula for an example gluon and an example pion were expressed (as much as possible) purely in exponentials, what would they each look like?

the reason for asking the question in this different way is because exponentials - e^ ( -i theta / 2pi) is a common recurring theme in *all* of the maths i have seen in the standard model and also the field of optics. it is the "common link".

i hope this is a challenging enough question to be interesting to some people, enough to want to explore. that is my strongest hope.